Name a classical monarchy, tyranny, or republic where the ruler does not have the right/ability to remove cabinet-level members of the government. Even in modern republics this is a standard thing. Pretty sure in modern monarchies most monarchs have the right as well, even if it's not practiced (due to possible protests against -them-).
The ruler should not have to call on the general membership to protest a person out of a position. The person could do an adequate enough job, but the purpose of a cabinet/council is historically to be a trusted group of advisers. i.e. a privy council.
Indeed, In Australia the Governor General, who is the Queens Representative has the power to dissolve the government, or more accurately dismiss the Prime Minister. It has happened only once in our history. In fact when you read their full powers they can appoint the Prime Minister as well, but by tradition they just give the position to the leader of the party that has the lower house majority.
